Solve m^22-i^21 - ScanMath

Question

Simplify the expression

2 m^{2} + 1

Evaluate

m^{2} \times 2 - i^{2} \times 1

Evaluate the power

m^{2} \times 2 - (- 1)

Use the commutative property to reorder the terms

2 m^{2} - (- 1)

Solution

2 m^{2} + 1

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Find the roots

m_{1} = - \frac{2}{2} i, m_{2} = \frac{2}{2} i

Alternative Form

m_{1} \approx - 0.707107 i, m_{2} \approx 0.707107 i

Evaluate

m^{2} \times 2 - i^{2} \times 1

To find the roots of the expression,set the expression equal to 0

m^{2} \times 2 - i^{2} \times 1 = 0

Evaluate the power

m^{2} \times 2 - (- 1) = 0

Use the commutative property to reorder the terms

2 m^{2} - (- 1) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 m^{2} + 1 = 0

Move the constant to the right-hand side and change its sign

2 m^{2} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

2 m^{2} = - 1

Divide both sides

\frac{2 m ^{2}}{2} = \frac{- 1}{2}

Divide the numbers

m^{2} = \frac{- 1}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

m^{2} = - \frac{1}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

m = \pm - \frac{1}{2}

Simplify the expression

More Steps

Evaluate

- \frac{1}{2}

Evaluate the power

\frac{1}{2} \times - 1

Evaluate the power

\frac{1}{2} \times i

Evaluate the power

More Steps

Evaluate

\frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

\frac{2}{2} i

m = \pm \frac{2}{2} i

Separate the equation into 2 possible cases

m = \frac{2}{2} i m = - \frac{2}{2} i

Solution

m_{1} = - \frac{2}{2} i, m_{2} = \frac{2}{2} i

Alternative Form

m_{1} \approx - 0.707107 i, m_{2} \approx 0.707107 i

Show Solution